TSTP Solution File: FLD058-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : FLD058-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:56:01 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 57
% Syntax : Number of formulae : 114 ( 29 unt; 6 typ; 0 def)
% Number of atoms : 621 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 906 ( 426 ~; 421 |; 0 &)
% ( 59 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 33 ( 33 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 319 ( 294 !; 0 ?; 319 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_or_equal_type,type,
less_or_equal: ( $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
( less_or_equal(a,b)
<=> less_or_equal(a,b) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_4) ).
tff(3,plain,
less_or_equal(a,b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( less_or_equal(additive_identity,a)
<=> less_or_equal(additive_identity,a) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
tff(6,plain,
less_or_equal(additive_identity,a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( less_or_equal(X,Z)
| ~ less_or_equal(X,Y) )
<=> ( ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ) )),
( ( less_or_equal(X,Z)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z) )
<=> ( ~ less_or_equal(X,Y)
| less_or_equal(X,Z)
| ~ less_or_equal(Y,Z) ) )),
rewrite(
( ( ~ less_or_equal(X,Y)
| less_or_equal(X,Z)
| ~ less_or_equal(Y,Z) )
<=> ( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) ) )),
( ( less_or_equal(X,Z)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z) )
<=> ( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [Z: $i,Y: $i,X: $i] :
( less_or_equal(X,Z)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [Z: $i,Y: $i,X: $i] :
( less_or_equal(X,Z)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
tff(12,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,b)
| less_or_equal(additive_identity,b) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,b)
| less_or_equal(additive_identity,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,b)
| less_or_equal(additive_identity,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,b)
| less_or_equal(additive_identity,b) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
less_or_equal(additive_identity,b),
inference(unit_resolution,[status(thm)],[18,15,6,3]) ).
tff(20,plain,
( defined(additive_identity)
<=> defined(additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
tff(22,plain,
defined(additive_identity),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
^ [X: $i] :
rewrite(
( ( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
tff(29,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[35,32,22]) ).
tff(37,plain,
( sum(additive_identity,b,additive_identity)
<=> sum(additive_identity,b,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_6) ).
tff(39,plain,
sum(additive_identity,b,additive_identity),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( sum(Y,X,Z)
| ~ sum(X,Y,Z) )
<=> ( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [Z: $i,Y: $i,X: $i] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [Z: $i,Y: $i,X: $i] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
tff(46,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,b,additive_identity)
| sum(b,additive_identity,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,b,additive_identity)
| sum(b,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,b,additive_identity)
| sum(b,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,b,additive_identity)
| sum(b,additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
sum(b,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[52,49,39]) ).
tff(54,plain,
^ [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
<=> ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
<=> ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
^ [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y) )
<=> ( ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U) )
<=> ( ~ less_or_equal(X,Y)
| less_or_equal(U,V)
| ~ sum(X,Z,U) ) )),
rewrite(
( ( ~ less_or_equal(X,Y)
| less_or_equal(U,V)
| ~ sum(X,Z,U) )
<=> ( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U) )
<=> ( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V)
| ~ sum(Y,Z,V) ) )),
rewrite(
( ( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) )
<=> ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
tff(60,plain,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(additive_identity,additive_identity)
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b) )
<=> ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(additive_identity,additive_identity)
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b)
| less_or_equal(additive_identity,additive_identity) )
<=> ( less_or_equal(additive_identity,additive_identity)
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b)
| less_or_equal(additive_identity,additive_identity) )
<=> ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(additive_identity,additive_identity)
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b)
| less_or_equal(additive_identity,additive_identity) )
<=> ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(additive_identity,additive_identity)
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b)
| less_or_equal(additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(additive_identity,additive_identity)
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,b) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
less_or_equal(additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[69,63,53,36,19]) ).
tff(71,plain,
( defined(b)
<=> defined(b) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
tff(73,plain,
defined(b),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(b)
| sum(additive_identity,b,b) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(b)
| sum(additive_identity,b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(b)
| sum(additive_identity,b,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(b)
| sum(additive_identity,b,b) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
sum(additive_identity,b,b),
inference(unit_resolution,[status(thm)],[76,32,73]) ).
tff(78,plain,
( ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(additive_identity,b,additive_identity)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity)
| ~ sum(additive_identity,b,b) )
<=> ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(additive_identity,b,additive_identity)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity)
| ~ sum(additive_identity,b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ~ sum(additive_identity,b,additive_identity)
| ~ sum(additive_identity,b,b)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity) )
<=> ( ~ sum(additive_identity,b,additive_identity)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity)
| ~ sum(additive_identity,b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(additive_identity,b,additive_identity)
| ~ sum(additive_identity,b,b)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity) )
<=> ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(additive_identity,b,additive_identity)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity)
| ~ sum(additive_identity,b,b) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(additive_identity,b,additive_identity)
| ~ sum(additive_identity,b,b)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity) )
<=> ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(additive_identity,b,additive_identity)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity)
| ~ sum(additive_identity,b,b) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(additive_identity,b,additive_identity)
| ~ sum(additive_identity,b,b)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(additive_identity,b,additive_identity)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,additive_identity)
| ~ sum(additive_identity,b,b) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
less_or_equal(b,additive_identity),
inference(unit_resolution,[status(thm)],[83,63,39,77,70]) ).
tff(85,plain,
( ~ sum(additive_identity,a,additive_identity)
<=> ~ sum(additive_identity,a,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(86,axiom,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
tff(87,plain,
~ sum(additive_identity,a,additive_identity),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
<=> ( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y) )
<=> ( ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) )),
( ( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) )
<=> ( ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y)
| ~ less_or_equal(Y,X) ) )),
rewrite(
( ( ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y)
| ~ less_or_equal(Y,X) )
<=> ( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) )),
( ( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) )
<=> ( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [Y: $i,X: $i] :
( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [Y: $i,X: $i] :
( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
tff(94,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| sum(additive_identity,a,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| sum(additive_identity,a,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ( ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity)
| sum(additive_identity,a,additive_identity) )
<=> ( sum(additive_identity,a,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity)
| sum(additive_identity,a,additive_identity) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| sum(additive_identity,a,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity)
| sum(additive_identity,a,additive_identity) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| sum(additive_identity,a,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity) ) ),
inference(transitivity,[status(thm)],[100,98]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity)
| sum(additive_identity,a,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| sum(additive_identity,a,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
~ less_or_equal(a,additive_identity),
inference(unit_resolution,[status(thm)],[103,97,6,87]) ).
tff(105,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
| ~ less_or_equal(a,b)
| ~ less_or_equal(b,additive_identity)
| less_or_equal(a,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
| ~ less_or_equal(a,b)
| ~ less_or_equal(b,additive_identity)
| less_or_equal(a,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
| ~ less_or_equal(a,b)
| ~ less_or_equal(b,additive_identity)
| less_or_equal(a,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z)
| less_or_equal(X,Z) )
| ~ less_or_equal(a,b)
| ~ less_or_equal(b,additive_identity)
| less_or_equal(a,additive_identity) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
$false,
inference(unit_resolution,[status(thm)],[107,15,3,104,84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : FLD058-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 03:23:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------